Knudsen number


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Knudsen number

In gas dynamics, the ratio of the molecular mean free path λ to some characteristic length L: Kn = λ/L. The length chosen will depend on the problem under consideration. It may be, for example, the diameter of a pipe or an object immersed in a flow, or the thickness of a boundary layer or a shock wave. See Mean free path

The magnitude of the Knudsen number determines the appropriate gas dynamic regime. When the Knudsen number is small compared to unity, of the order of Kn ≤ 0.1, the fluid can be treated as a continuous medium and described in terms of the macroscopic variables: velocity, density, pressure, and temperature. In the transition flow regime, for Knudsen numbers of the order of unity or greater, a microscopic approach is required, wherein the trajectories of individual representative molecules are considered, and macroscopic variables are obtained from the statistical properties of their motions. In both internal and external flows, for Kn ≥ 10, intermolecular collisions in the region of interest are much less frequent than molecular interactions with solid boundaries, and can be ignored. Flows under such conditions are termed collisionless or free molecular. In the range 0.1 ≤ Kn ≤ 1.0, termed the slip flow regime, it is sometimes possible to obtain useful results by treating the gas as a continuum, but allowing for discontinuities in velocity and temperature at solid boundaries. See Gas dynamics, Kinetic theory of matter, Rarefied gas flow

Knudsen number

[kə′nüd·sən ‚nəm·bər]
(fluid mechanics)
The ratio of the mean free path length of the molecules of a fluid to a characteristic length; used to describe the flow of low-density gases.
References in periodicals archive ?
The slip correction factor has been investigated at reduced pressures and high Knudsen number using polystyrene latex (PSL) particles.
In 1910, Cunningham [1] derived a correction factor, (1 + A * Kn) including a positive parameter A, for the Stokes drag force required to maintain the fluid velocity in the high Knudsen number regime.
The values were found to agree with the predicted low and high Knudsen number limits to within the experimental relative uncertainty of [+ or -]2%.
Their measurements covered a Knudsen number range from 0.
He then used the oil-drop works of Eglin [14] and Millikan [4] for slip correction data over a wide range of Knudsen number (0.
The 20 nm, 100 nm, and 270 nm diameter particles studied here span much of the Knudsen number region of interest.
491, with the caution that others using our results for the slip correction parameter must use the same definition of the mean free path when computing the Knudsen number.
This correction is important for the slip correction measurements in the high Knudsen number regime because the measured voltages are small.
The calculations for both the slip correction factor and the Knudsen number require knowing what the diameters of these particles are.
In the limit of large Knudsen number, C is large compared to 1, simplifying Eq.
015 with the exception of the two points at Knudsen number less than 1.
The parameter [delta] corresponds to the asymptotic value of [alpha] + [beta] and is expected to be accurately determined from our experiments with much of the data in the large Knudsen number regime.